How to curve just one face
A different approach (than my other answer)  would be to modify the mesh slightly so that you could perform a bevel operation.

Beveling rounds off a corner, so you need a corner where you want the rounded part instead of a flat face.  I accomplished this by connecting the two edges across the face and moving the new edge to a positing where it's two adjoining faces are at right angles.



You can then select the new edge and hit Ctrl+B to bevel the edge into a curve, using the mouse wheel to control the number of subdivisions.